Abstract Algebra: Theory and Applications · Problem 17.5.2

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · polynomial-arithmetic

Problem

Compute each of the following. ((a)) (5x2+3x−4)+(4x2−x+9)(5x^2 + 3x - 4) + (4x^2 - x + 9) in Z12[x]\mathbb{Z}_{12}[x] ((b)) (5x2+3x−4)(4x2−x+9)(5x^2 + 3x - 4)(4x^2 - x + 9) in Z12[x]\mathbb{Z}_{12}[x] ((c)) (7x3+3x2−x)+(6x2−8x+4)(7x^3 + 3x^2 - x) + (6x^2 - 8x + 4) in Z9[x]\mathbb{Z}_9[x] ((d)) (3x2+2x−4)+(4x2+2)(3x^2 + 2x - 4) + (4x^2 + 2) in Z5[x]\mathbb{Z}_5[x] ((e)) (3x2+2x−4)(4x2+2)(3x^2 + 2x - 4)(4x^2 + 2) in Z5[x]\mathbb{Z}_5[x] ((f)) (5x2+3x−2)2(5x^2 + 3x - 2)^2 in Z12[x]\mathbb{Z}_{12}[x] Hint. (a) 9x2+2x+59x^2 + 2x + 5; (b) 8x4+7x3+2x2+7x8x^4 + 7x^3 + 2x^2 + 7x.

Related theory

Browse the problem library